Exploring optical dielectric function of impurity doped quantum dots under combined influence of hydrostatic pressure and temperature and in presence of noise

Accepted Manuscript Exploring optical dielectric function of impurity doped quantum dots under combined influence of hydrostatic pressure and temperature and in presence of noise Aindrila Bera, Manas Ghosh PII: DOI: Reference:

S0009-2614(16)30923-X http://dx.doi.org/10.1016/j.cplett.2016.11.035 CPLETT 34342

To appear in:

Chemical Physics Letters

Received Date: Accepted Date:

7 October 2016 17 November 2016

Please cite this article as: A. Bera, M. Ghosh, Exploring optical dielectric function of impurity doped quantum dots under combined influence of hydrostatic pressure and temperature and in presence of noise, Chemical Physics Letters (2016), doi: http://dx.doi.org/10.1016/j.cplett.2016.11.035

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Exploring optical dielectric function of impurity doped quantum dots under combined influence of hydrostatic pressure and temperature and in presence of noise Aindrila Bera and Manas Ghosh

∗†‡

Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731235, West Bengal, India.

Abstract We investigate the total optical dielectric function (TODF) of impurity doped QDs under the combined influence of hydrostatic pressure (HP) and temperature and in presence of Gaussian white noise. Noise has been incorporated to the system additively and multiplicatively. Variations of HP, temperature and noise strength affect TODF profile in subtle way. And the subtlety also depends on mode of application of noise. Extrapolation of the present study would be important in understanding the effective optical properties of the system under given conditions of HP and temperature and in presence of noise. Keywords: quantum dot; impurity; optical dielectric function; hydrostatic pressure; temperature; Gaussian white noise

∗ † ‡

e-mail address: [email protected] Phone: (+91) (3463)261526, (3463)262751-6 (Ext.467) Fax: +91 3463 262672

1

I.

INTRODUCTION

It appears needless to mention that the low-dimensional semiconductor systems (LDSS) e.g. quantum wells (QWLs), quantum wires (QWRs) and quantum dots (QDs) have become part and parcel of applications in the field of applied physics. Existence of strong confinement in LDSS compared with their bulk analogues has motivated intense research activities in studying their electronic, magnetic, and optical properties, both experimentally and theoretically [1]. Presence of shallow impurity states in LDSS causes dramatic alteration of their optical, magnetic and transport properties [2–4]. As a result, we can find ever-increasing research on impurity states of LDSS in view of elucidating of a lot of physical properties [5–12]. External perturbations, such as electric field, magnetic field, hydrostatic pressure (HP), and temperature render important information about nonlinear optical (NLO) properties of LDSS [13–27]. High pressure investigations of LDSS deserve special significance in the realm of condensed matter physics and materials sciences because of their tremendous influence on the tunable optical properties relevant to applications in optoelectronics, QD lasers, high-density memory, bio-engineering etc. [28, 29]. HP, therefore, stands as a prolific tool to fine-tune the electron-related NLO properties of LDSS. As a natural follow-up several crucial studies on LDSS under HP have been performed by various research groups [30–43]. In addition to HP, temperature effects also tailor the electronic structure of LDSS [29] and consequently the NLO properties which bear close correspondence with the electron-impurity interaction [35, 36, 41, 42, 44–48]. Recently, we have made a detailed exploration of a few NLO properties of doped QD under the combined influence of HP and temperature and in presence of noise [49]. In the current manuscript we investigate the simultaneous influence of hydrostatic pressure and temperature on optical dielectric function (ODF) of doped QD in presence of Gaussian white noise. The motivation behind the work stems from a recent important study carried out by Vahdani on ODF [50]. Determination of ODFs is crucial to account for dielectric mismatch between QD and the surrounding medium (the matrix). As a result of such mismatch the optical properties are affected and the changed values of the optical properties are directly measurable. Moreover, from the knowledge of linear and third-order nonlinear ODFs it is possible to evaluate the effective dielectric function [ef f (ν)] of the dot-matrix composite 2

system absorbing the influence of dielectric mismatch between the dot and the matrix. Thus, in practice, determination of ODF assumes unquestionable significance since an extended study which originates from these ODF values would lead to understanding the effective optical properties of the composite systems arising out of dielectric mismatch. However, for that purpose one has to envisage an ensemble of QDs (e.g. GaAs) randomly dispersed amidst some surrounding medium (the matrix). And the QDs would have to be regarded as quite distant from each other to ignore any kind of inter-dot electron tunneling. As a result, electronic structure of each QD can be determined independently [50]. However, the study of ODF under the combined influence of hydrostatic pressure and temperature and in presence of noise still remains unexplored. In the present work we have calculated the total optical dielectric function (TODF) [(ν)] which is a combination of linear [(1) (ν)] and the third-order nonlinear [(3) (ν)] ODFs. The system under investigation is a 2-d QD (GaAs) which contains only one electron and subject to parabolic confinement in the x − y plane. The dopant impurity is represented by a Gaussian potential. An orthogonal magnetic field is also present which provides an extra confinement. The system is further exposed to an external static electric field. Incorporation of Gaussian white noise to the system has been done through two different pathways (modes) viz. additive and multiplicative [11, 49]. The study reveals elegant interplay among HP, temperature and noise that ultimately settles the ODF profiles of doped QD systems.

II.

METHOD

We consider QD system doped with impurity. It is exposed to external static electric field (F ) applied along x and y-directions. In addition to this noise (additive/multiplicative) is applied to the system. Thus, the system Hamiltonian is given by H0 = H00 + Vimp + |e|F (x + y) + Vnoise .

(1)

Within effective mass approximation, H00 stands for QD without impurity containing single carrier electron. The system is subject to lateral parabolic confinement in the x − y plane. An orthogonal perpendicular magnetic field is also present. V (x, y) = 12 m∗ ω02 (x2 + y 2 ) is the confinement potential with ω0 as the harmonic confinement frequency. H00 , thus, can also

3

be written as H00 =

1 h e i2 1 ∗ 2 2 −i~∇ + A + m ω0 (x + y 2 ). 2m∗ c 2

(2)

m∗ represents the effective mass of the electron inside the QD material. Working in Landau gauge [A = (By, 0, 0), where A is the vector potential and B is the magnetic field strength], H00 reads

ωc =

eB m∗ c

~2 =− ∗ 2m



∂2 ∂2 + ∂x2 ∂y 2



1 1 ∂ + m∗ ω02 x2 + m∗ (ω02 + ωc2 )y 2 − i~ωc y , (3) 2 2 ∂x p being the cyclotron frequency, where c is the velocity of light. Ω = ω02 + ωc2 can

H00

be viewed as the effective confinement frequency in the y-direction. In presence of HP and temperature, the effective mass becomes pressure and temperaturedependent and is given by (for GaAs) [1] ∗



m (P, T ) = m0 1 +

EPΓ



2 1 + Γ Γ Eg (P, T ) Eg (P, T ) + ∆0

−1 ,

(4)

where m0 is the single electron bare mass. EPΓ = 7.51 eV is the energy related to momentum matrix element. ∆0 = 0.341 eV is the spin-orbit splitting of the valence band (VB) for GaAs. The pressure and temperature-dependent energy gap for GaAs QD at Γ point in units of eV is given by EgΓ (P, T ) = EgΓ (0, T ) + 1.26 × 10−2 P − 3.77 × 10−5 P 2 , in the above expression P is in Kbar unit and the factors 1.26 × 10−2 and 3.77 × 10−5 have units eV/Kbar and eV/Kbar2 , respectively. EgΓ (0, T ) is the energy gap at zero pressure and is given by EgΓ (0, T ) = 1.519 −

5.405 × 10−4 T 2 . T + 204

The Pressure and temperature-dependent dielectric constant (for GaAs) is given by [1]     (P, T ) = 12.74 exp −1.73 × 10−3 P . exp 9.4 × 10−5 (T − 75.6) , for T ≤ 200K, (5) and     (P, T ) = 13.18 exp −1.73 × 10−3 P . exp 20.4 × 10−5 (T − 300) , for T > 200K. (6) 4

Vimp is the Gaussian impurity (dopant) potential [11, 49] given by Vimp = 2 2 V0 e−γ [(x−x0 ) +(y−y0 ) ] . (x0 , y0 ), V0 and γ −1/2 are the site of dopant incorporation, strength of the dopant potential, and the spatial spread of impurity potential, respectively. γ can be written as γ = kε, where k is a constant and ε is the static dielectric constant of the medium. The term Vnoise [cf. eqn.(1)] stands for white noise [f (x, y)] which follows a Gaussian distribution (generated by Box-Muller algorithm), has a strength ζ and is characterized by zero-average and spatial δ-correlation conditions [11, 49]. Such white noise can be introduced to the system via two different modes (pathways) i.e. additive and multiplicative [11, 49]. These two different modes can be discriminated on the basis of extent of system-noise interaction. The time-independent Schr¨odinger equation has been solved by generating the sparse Hamiltonian matrix (H0 ). The various matrix elements include the function ψ(x, y), which is a linear combination of the products of harmonic oscillator eigenfunctions. In the computation we have used sufficient number of basis functions that satisfy the convergence test. H0 is diagonalized afterwards in the direct product basis of harmonic oscillator eigenfunctions to obtain the energy levels and wave functions. We now consider interaction between a polarized monochromatic electromagnetic field of angular frequency ν with an ensemble of QDs. If the wavelength of progressive electromagnetic wave is greater than the QD dimension, the amplitude of the wave may be regarded constant throughout QD and the aforesaid interaction can be realized under electric dipole approximation. Now, the electric field of incident optical wave can be expressed as h i   ˆ ˜ iνt + E˜ ∗ e−iνt k. E(t) = E(t)kˆ = 2E˜ cos (νt) kˆ = Ee

(7)

Following Vahdani, by means of density matrix approach and iterative procedure, considering optical transition between two states |ψ0 i and |ψ1 i, the linear [χ(1) (ν)] and the third-order nonlinear [χ(3) (ν)] electric susceptibilities can be written as [50] χ(1) (ν) =

σs |M01 |2 , E01 − ~ν − i~Γ

5

(8)

and ˜2  σs |M01 |2 |E| 4|M01 |2 χ (ν) = − . E01 − ~ν − i~Γ (E01 − ~ν)2 + (~Γ)2 # 2 (M11 − M00 ) − . (E01 − i~Γ) (E01 − ~ν − i~Γ) (3)

(9)

As stated by Vahdani, the linear and third-order nonlinear ODFs are related to χ(1) (ν) and χ(3) (ν) as follows [50]: (1) (ν) = 1 + 4πχ(1) (ν),

(10)

(3) (ν) = 4πχ(3) (ν).

(11)

(ν) = (1) (ν) + (3) (ν),

(12)

and

The TODF is given by

where σs is the carrier density, M01 = ehψ0 |ˆ x + yˆ|ψ1 i is the matrix element of the dipole moment, ψi (ψj ) are the eigenstates and E01 = (E1 − E0 ) is the energy difference between these states, Γ is the off-diagonal relaxation rate.

III.

RESULTS AND DISCUSSION

The calculations are performed using the following parameters: ε = 12.4 (without considering pressure and temperature dependence), m∗ = 0.067m0 (without considering pressure and temperature dependence), where m0 is the free electron mass. Confinement potential: ~ω0 = 250.0 meV, electric field strength: F = 100 KV/cm, magnetic field strength: B = 20.0 T, noise strength: ζ = 1.0 × 10−8 , dopant potential: V0 = 280.0 meV, and σs = 5.0 × 1024 m−3 . The parameters are suitable for GaAs QDs.

A.

Effect of hydrostatic pressure:

Fig. 1a exhibits the TODF profiles against incident photon energy hν at four different values of HP viz. P = 0 Kbar, 50 Kbar, 100 Kbar, and 200 Kbar in absence of noise. 6

Temperature has been kept fixed at T = 100 K. The TODF peaks exhibit red-shift with increase in HP. Moreover, the peak height decreases with increase in HP. However, the peak shift ceases from P = 100 Kbar onwards. The observations indicate that, in absence of noise, an increase in pressure reduces the energy interval between the concerned eigenstates and also depletes the mutual overlap between them. However, the energy interval acquires some steady value as pressure exceeds a value of 100 Kbar and the peak shift does not occur henceforth. Fig. 1b and 1c represent the similar profiles in presence of additive a)

(i) (ii)

10

20 (ii)

(i) (ii) (iii)

(i)

15 (iii)





15

b)

(i) (ii) (iii) (iv)

20

(iii)

10

(iv)

5

5

0 0

100

200

0

300

0

81

h(meV)

c)

163

244

325

h (meV)

18

d) (i) (ii) (iii)

(ii)

14

(i) (ii) (iii)

20

(i)

9





(i) (iii)

18

(ii)

16

5

(iii)

14

0 0

88

175

263

351

0

h(meV)

50

100

150

200

250

P (Kbar)

FIG. 1: Plots of TODF vs hν at T = 100 K: (a) in absence of noise at (i) P = 0 Kbar, (ii) P = 50 Kbar, (iii) P = 100 Kbar and (iv) P = 200 Kbar, (b) in presence of additive noise at (i) P = 0 Kbar, (ii) P = 100 Kbar and (iii) P = 200 Kbar, (c) in presence of multiplicative noise at (i) P = 0 Kbar, (ii) P = 100 Kbar and (iii) P = 200 Kbar and (d) Plot of TODF vs P at T = 100 K: (i) in absence of noise, (ii) in presence of additive noise and (iii) in presence of multiplicative noise.

and multiplicative noise, respectively. In both the cases, just like noise-free situation, the TODF peak height decreases with increase in HP. However, unlike noise-free situation, the

7

TODF peaks remain unshifted with increase in pressure right from zero pressure situation. The observations, therefore, suggest that, in presence of noise (regardless of its mode of application) an increase in HP diminishes the extent of mutual overlap between the relevant wave functions. However, an increase in HP does not affect the energy interval leading to unshifted TODF peaks. In order to envisage comparative TODF profiles in absence and in presence of noise; we now plot TODF against HP in absence of noise [fig. 1d(i)] and in presence of additive [fig. 1d(ii)] and multiplicative [fig. 1d(iii)] noise, respectively, at a given frequency of the external field. Under all conditions TODF profiles delineate persistent drop as HP increases. However, the TODF values prominently depend on presence of noise as well as on its mode of application. The TODF displays highest value in absence of noise and lowest value in presence of multiplicative noise. TODF values in presence of additive noise lie in between them. The observation nicely supports the previous findings as we find that an enhancement in HP would persistently deplete the extent of overlap between the relevant eigenstates. Furthermore, introduction of noise has been found to diminish the said overlap from that of noise-free condition and the drop becomes more severe with multiplicative noise. However, introduction of noise does not bring about any qualitative change in the overall TODF profile from that of noise-free situation.

B.

Effect of temperature:

Fig. 2a displays the TODF profiles against incident photon energy hν at three different values of temperature viz. T = 0 K, 100 K and 200 K in absence of noise. The HP has been kept fixed at P = 50 Kbar. Although the TODF peak height decreases with increase in temperature but the peak position remains unshifted. Moreover, the extent of drop in the peak height with increase in temperature is quite mild in comparison with what has been found with increase in HP. The observations suggest that, in absence of noise, an increase in temperature reduces the mutual overlap between the pertinent eigenstates. However, the said increase in temperature remains indifferent towards the energy interval between the eigenstates. Fig. 2b and 2c delineate the similar profiles in presence of additive and multiplicative noise, respectively. In both the cases, just like noise-free situation, the TODF peak height 8

a) 18

18

(i) (ii) (iii)

(i) (ii)

15

(i)

b)

(iii)

(iii)

12

ε (ν)

ε (ν)

12 9

9

6

6

3

3

0 0

75

150

225

0

300

0

83

167

hν (meV)

250

333

hν (meV)

16

20 (i)

c) 12

d)

(i) (ii) (iii)

(ii)

(i)

16

(iii)

8

ε (ν)

ε (ν)

(i) (ii) (iii)

(ii)

15

(ii)

12 (i) (ii) (iii)

4 (iii)

8 0 0

64

127

191

255

318

0

hν (meV)

100

200

300

400

500

T (K)

FIG. 2: Plots of TODF vs hν with P = 50 Kbar: (a) in absence of noise, (b) in presence of additive noise and (c) in presence of multiplicative noise at; (i) T = 0 K, (ii) T = 100 K and (iii) T = 200 Kbar, (d) Plot of TODF vs T at P = 50 Kbar: (i) in absence of noise, (ii) in presence of additive noise and (iii) in presence of multiplicative noise.

decreases with increase in temperature with unshifted peak-position. Thus, application of noise does not bring about any characteristic change in the overall TODF profile as long as temperature variation is concerned. This is true for both the modes of application of noise. During temperature variation, application of noise only causes quantitative change in the TODF profile from that of noise-free condition which noticeably depends on mode of application of noise. In view of this fig. 2d depicts the TODF against temperature in absence of noise [fig. 2d(i)] and in presence of additive [fig. 2d(ii)] and multiplicative [fig. 2d(iii)] noise, respectively, at a given frequency of the external field. Under all conditions TODF profiles exhibit steady fall as temperature increases with clear dependence of its magnitude on presence of noise as well as on its mode of application. The TODF displays largest value

9

in absence of noise and smallest value in presence of multiplicative noise. TODF values in presence of additive noise lie in between them. The observation indicates that an increase in temperature regularly diminishes the extent of overlap between the relevant eigenstates. Additionally, ingression of noise depletes the said overlap from that of noise-free condition and the drop becomes more intense with multiplicative noise.

C.

Role of noise strength:

Discussions hitherto made necessitate the exploration of role of noise strength on TODF profile at given values of temperature and HP. During both temperature and pressure variations we observe a definite sequence viz.

TODF (in absence of noise) >

TODF (in presence of additive noise) > TODF (in presence of multiplicative noise). And the sequence can be realized (as we have already mentioned), if we think in terms of extent of overlap between the pertinent wave functions. As a natural follow-up, at the close of our discussion we would like to concentrate on the important aspect of how TODF changes as noise strength (ζ) is varied over a range under a given temperature and pressure. Fig. 3 delineates the variation of TODF with −log(ζ) in presence of additive [fig. 3(i)] and multiplicative [fig. 3(ii)] noise, respectively, at T = 100 K and pressure P = 50 Kbar. We have 20 (noise-free value)

ε (ν)

15

(i) (ii)

10

5

(i) (ii)

0 2

4

6

8

10

12

-log(ζ)

FIG. 3: Plots of TODF vs −log(ζ) at T = 100 K and P = 50 Kbar: (i) in presence of additive noise and (ii) in presence of multiplicative noise.

changed noise strength over a range from ζ = 1.0 × 10−12 to ζ = 1.0 × 10−2 and the TODF values at the lowest segment of the range nearly represent those under noise-free condition. 10

Fig. 3 shows that TODF declines persistently (from the noise-free value) with increase in the noise strength for both additive and multiplicative noise. However, throughout the entire range of ζ TODF profile registers higher magnitude in presence of additive noise than its multiplicative neighbor. It thus appears that progressive augmentation in the extent of noise applied to the system diminishes the TODF of doped QD system. And the diminish becomes more evident with multiplicative noise owing to its close linkage with system coordinates.

IV.

CONCLUSION

The TODF profile of impurity doped QDs under the combined influence of HP and temperature has been examined in presence and absence of Gaussian white noise. As a general feature we have observed that an increase in either temperature or pressure decreases TODF. Moreover, introduction of noise also diminishes TODF from noise-free value and the diminish becomes more profound in presence of multiplicative noise. It has been further observed that only in absence of noise, the TODF peaks exhibit red-shift with increase in pressure. However, variation of temperature and presence of noise do not affect the energy interval and TODF peaks refrain from showing any kind of shift. An extension of the present study would be helpful in understanding the effective optical properties of the system under given conditions of HP and temperature and in presence of noise.

V.

ACKNOWLEDGEMENTS

The authors A. B. and M. G. thank D. S. T-F. I. S. T (Govt. of India) and U. G. C.- S. A. P (Govt. of India) for support.

[1] L. Lu, W. Xie, Z. Shu, Physica B 406 (2011) 3735-3740. [2] G. Rezaei, S. Shojaeian Kish, Superlattices and Microstructures 53 (2013) 99-112. [3] C. Dane, H. Akbas, A. Guleroglu, S. Minez, K. Kasapo˘glu, Physica E 44 (2011) 186-189. [4] A. Sali, H. Satori, Superlattices and Microstructures 69 (2014) 38-52. [5] S. Yilmaz, M. S ¸ ahin, Phys. Status Solidi B 247 (2010) 371-374.

11

˙ Karabulut, U. ¨ Atav, H. S [6] I. ¸ afak, M. Tomak, Eur. Phys. J. B 55 (2007) 283-288. ¨ ¨ Atav, Optics Commun. 282 (2009) 3999-4004. [7] A. Ozmen, Y. Yakar, B. C ¸ akir, U. ¨ ¨ ur Sezer, M. S¸ahin, Superlattices and Microstructures [8] B. C ¸ akir, Y. Yakar, A. Ozmen, M. Ozg¨ 47 (2010) 556-566. [9] F. Qu, F. V. Moura, F. M. Alves, R. Gargano, Chem. Phys. Lett. 561-562 (2013) 107-114. [10] R. K. Hazra, M. Ghosh, S. P. Bhattacharyya, Chem. Phys. Lett. 468 (2009) 216-221. [11] S. Saha, J. Ganguly, S. Pal, M. Ghosh, Chem. Phys. Lett. 658 (2016) 254-258. [12] M. R. K. Vahdani, G. Rezaei, Phys. Lett. A 373 (2009) 3079-3084. [13] M. Kirak, S. Yilmaz, M. S ¸ ahin, M. Gen¸casian, J. Appl. Phys. 109 (2011) 094309. [14] F. Ungan, U. Yesilgul, E. Kasapoglu, H. Sari, I. S¨okmen, J. Lumin. 132 (2012) 1627-1631. [15] I. Karabulut, S. Baskoutas, J. Appl. Phys. 103 (2008) 073512 (5 pages). [16] S. Baskoutas, C. S. Garoufalis, A. F. Terzis, Eur. Phys. J. B 84 (2011) 241-247. [17] S. Baskoutas, E. Paspalakis, A. F. Terzis, J. Phys:Cond. Mat. 19 (2007) 395024 (9-pages). [18] C. A. Duque, M. E. Mora-Ramos, E. Kasapoglu, F. Ungan, U. Yesilgul, S. S¸akiro˘glu, H. Sari, I. S¨okmen, J. Lumin. 143 (2013) 304-313. [19] S. S¸akiro˘ glu, F. Ungan, U. Yesilgul, M. E. Mora-Ramos, C. A. Duque, E. Kasapoglu, H. Sari, I. S¨okmen, Phys. Lett. A 376 (2012) 1875-1880. [20] H. Hassanabadi, G. Liu, L. Lu, Solid State Commun. 152 (2012) 1761-1766. [21] B. Chen, K. -X. Guo, R. -Z. Wang, Y. -B. Zheng, B. Li, Eur. Phys. J. B 66 (2008) 227-233. [22] B. Li, K. -X. Guo, Z. -L. Liu, Y. -B. Zheng, Phys. Lett. A 372 (2008) 1337-1340. [23] R. Khordad, Physica B 407 (2012) 1128-1133. [24] A. Hakimyfard, M. G. Barseghyan, A. A. Kirakosyan, Physica E 41 (2009) 1596-1599. [25] A. J. Peter, Solid State Commun. 147 (2008) 296-300. [26] C. A. Duque, N. Porras-Montenegro, Z. Barticevic, M. Pacheco, L. E. Oliveira, J. Phys.: Condens. Matter 18 (2006) 1877-1884. [27] G. Rezaei, S. S. Kish, Physica E 45 (2012) 56-60. [28] M. Zuhair, Physica E 46 (2012) 232-235. [29] M. Kirak, Y. Altinok, S. Yilmaz, The J. Lumin. 136 (2013) 415-421. ¨ Atav, H. S [30] I. Karabulut, U. ¸ afak, M. Tomak, Physica B 393 (2007) 133-138. [31] C. -X. Xia, Y. Liu, S. Wei, Appl. Surf. Sci. 254 (2008) 3479-3483. [32] C. -X. Xia, F. Jiang, S. Wei, Superlattices and Microstructures 43 (2008) 285-291.

12

[33] N. Eseanu, E. C. Niculescu, L. M. Burileanu, Physica E 41 (2009) 1386-1392. [34] E. C. Niculescu, N. Eseanu, Eur. Phys. J. B 75 (2010) 247-251. [35] A. Hakimyfard, M. G. Barseghyan, C. A. Duque, A. A. Kirakosyan, Physica B 404 (2009) 5159-5162. [36] M. G. Barseghyan, A. Hakimyfard, S. Y. L´opez, C. A. Duque, A. A. Kirakosyan, Physica E 43 (2010) 529-533. [37] A. M. Elabsy, Physica Scripta 48 (1993) 376-378. [38] A. J. Peter, Physica E 28 (2005) 225-229. [39] S. T. Perez-Merchancano, H. Paredes-Gutierrez, J. Silva-Valencia, J. Phys.: Condens. Matter 19 (2007) 0262. [40] S. T. Perez-Merchancano, R. Franco, J. Silva-Valencia, Microelectronic J. 39 (2008) 383-386. [41] S. Liang, W. Xie, Physica B 406 (2011) 2224-2230. [42] S. J. Liang, W. Xie, Eur. Phys. J. B 81 (2011) 79-84. [43] S. Y. L´ opez, N. Porras-Montenegro, C. A. Duque, Physica B 362 (2005) 41-49. [44] P. Ba¸ser, I. Altuntas, S. Elagoz, Superlattices and Microstructures 92 (2016) 210-216. [45] H. D. Karki, S. Elagoz, P. Ba¸ser, Superlattices and Microstructures 48 (2010) 298-304. [46] A. M. Elabsy, Physica Scripta 59 (1999) 328-330. [47] R. Khordad, Physica E 41 (2009) 543-547. [48] L. Bouza¨ıene, H. Alamri, L. Sfaxi, H. Maaref, J. Alloys and Compounds 655 (2016) 172-177. [49] J. Ganguly, S. Saha, A. Bera, M. Ghosh, Superlattices and Microstructures 98 (2016) 385-399. [50] M. R. K. Vahdani, Superlattices and Microstructures 76 (2014) 326-338.

13

Figure Captions fig. 1: Plots of TODF vs hν at T = 100 K: (a) in absence of noise at (i) P = 0 Kbar, (ii) P = 50 Kbar, (iii) P = 100 Kbar and (iv) P = 200 Kbar, (b) in presence of additive noise at (i) P = 0 Kbar, (ii) P = 100 Kbar and (iii) P = 200 Kbar, (c) in presence of multiplicative noise at (i) P = 0 Kbar, (ii) P = 100 Kbar and (iii) P = 200 Kbar and (d) Plot of TODF vs P at T = 100 K: (i) in absence of noise, (ii) in presence of additive noise and (iii) in presence of multiplicative noise. fig. 2: Plots of BE vs T at (i) P = 0 Kbar, (ii) P = 25 Kbar, (iii) P = 200 Kbar: (a) under noise-free condition, (b) in presence of additive noise and (c) in presence of multiplicative noise, (d) similar plot at P = 25 Kbar (i) under noise-free condition, (ii) in presence of additive noise and (iii) in presence of multiplicative noise. fig. 3: Plots of TODF vs −log(ζ) at T = 100 K and P = 50 Kbar: (i) in presence of additive noise and (ii) in presence of multiplicative noise.

14

Research Highlights



Total optical dielectric function (TODF) of doped quantum dot is studied.



Hydrostatic pressure (HP) and temperature (T) affect TODF.



The dot is subjected to Gaussian white noise.



Noise can tailor the TODF depending on mode of application.

Graphical Abstract

(i) noise-free (ii) additive noise (iii) multiplicative noise

20

ε (ν)

(i)

18

(ii)

16

(iii)

14 0

50

100

150

P (Kbar)

200

250